The scaling procedure used in Section REF  is to choose \(\gamma \)  in \(\ell (\theta ; \mathbf {y}) = \gamma \ell _{TW}(\theta ; \mathbf {y})\)  so that the generalised posterior variance of \(\theta \)  is equal to the asymptotic variance of \(\hat{\theta }_{TW}\) . However this is only suitable for a \(p=1\)  parameter as it would be impossible to choose \(\gamma \)  to equate \(p\)  general posterior and asymptotic variances. Instead, we consider two approaches previously used in the composite likelihood literature [1]}. The first chooses \(\gamma \)  to ensure the expectation of a quantity analogous to the likelihood ratio statistic converges to \(p\)  (the expectation of the likelihood ratio statistic). The second scales the curvature of the generalised likelihood so that the asymptotic generalised posterior variance is equal to the asymptotic variance of \(\hat{\theta }_{TW}\) .
